High toric power ophthalmic lenses

ABSTRACT

An ophthalmic aberration corrected toric lens which is derived from a basic toric lens, said basic lens having on a block of refringent material a spherical refracting surface and a toric refracting surface, said basic lens further having first and second main meridian planes at right angles to one another, said ophthalmic aberration corrected toric lens having on a block of the said refracting material two opposite refracting surfaces one of which is identical to one of the two refracting surfaces of said basic lens, while the other refracting surface of said aberration corrected ophthalmic lens is a so-called aberration minimizing surface and is shaped to maintain astigmatism and field curvature aberrations of said ophthalmic lens less than + OR - 0.50 Diopters.

Unite States 1- atent 91 Tagnon 1 Mar. 27, 1973 [76] Inventor: Luc Andre Marcel Tagnon, 6 rue Pastourelle, Paris, France [22] Filed: Oct. 18, 1971 [21] Appl. No.: 190,058

Related U.S. Application Data [63] Continuation-impart of Ser. No. 771,143, Oct. 28,

1968, abandoned.

[30] Foreign Application Priority Data 1/1966 Feinbloom ..351/160 Primary Examiner-David H. Rubin Att0rneyRobert E. Burns et al.

[57] ABSTRACT An ophthalmic aberration corrected toric lens which is derived from a basic toric lens, said basic lens having on a block of refringent material a spherical refracting surface and a toric refracting surface, said basic lens further having first and second main meridian planes at right angles to one another, said ophthalmic aberration corrected toric lens having on a block of the said refracting material two opposite refracting surfaces one of which is identical to one of the two refracting surfaces of said basic lens, while the other refracting surface of said aberration corrected ophthalmic lens is a so-called aberration minimizing surface and is shaped to maintain astigmatism and field curvature aberrations of said ophthalmic lens less than i 0.50 Diopters.

9 Claims, 18 Drawing Figures PATENTEEmzmu SkiEET OlUF 1O PATENTEDmzmzs 3,722,985

sum 05 0F 10 M2- 16,001) r2. 504.00 mm l l l 56 62 66 74 6a 86 PATEhHI-mznm; 3,722,986

sum 070F 10 PATENTEEmzmn SHEET UBUF 10 HIGH TORIC POWER OPHTHALMIC LENSES This application is a continuation-in-part application of the now abandoned patent application serial No. 771,143; filed Oct. 28, 1968, by the same applicant as that of the present invention.

BACKGROUND OF THE INVENTION This invention relates in general to ophthalmic high power lenses and has reference more particularly to improvements in ophthalmic toric lenses.

When the eye before which an ophthalmic lens is placed utilizes a peripheral zone thereof, aberrations, astigmatism and notably field curvature appear and reduce the quality of the eye ametropia correction.

In practice, this defect is negligible in the case of negative power lenses and low positive power lenses, provided that these lenses have a suitable curvature. On the other hand, it limits the useful vision of an eye provided with a high-power positive lens, for the higher the lens power the smaller the useful area of the lens.

It is known to resort to aspheric surfaces for reducing these aberrations. The term aspheric usually denotes surfaces of revolution such as paraboloids and ellipsoids, for example, obtained by causing the same parabolic or elliptic curve to rotate about the axis of the lens. These surfaces are currently used in instrumental optics. They permit a certain correction of the aberrations of ophthalmic lenses when these are designed for a single type of vision, for instance distant vision. Moreover, making such surfaces requires such elaborate machines and processes that their cost is very expensive. Finally, in many cases the human eye suffers from astigmatism, for example the post-operative residual corneal astigmatism of a patient operated for cataract, which entails the use of toric lenses, for example toric lenses having a spheric radius-+1200 and a cylindrical radius 3.00. It will be readily understood that hitherto known aspheric surfaces of revolution are not capable of correcting such lenses in a very satisfactory manner. Either one main meridian will be properly corrected for aberrations but not the other, or the aspheric surface of revolution is designed to correct the aberrations in a mean meridian but it leaves still too important aberrations uncorrected in the main meridians.

On the other hand the applicant has been producing for more than ten years progressive ophthalmic lenses. This type of lens usually comprises, on a block of refringent material, two opposite refracting surfaces: a first conventional refracting spherical or toroidal surface and a second refracting surface, so called progressive surface. This progressive surface cannot be simply described in terms of circle, ellipse, etc.

Elementary optical calculation adapted to the manufacturing processes permits to determine such progressive surfaces point by point and to produce them at an economical industrial scale as follows:

Every point A, of the desired progressive surface is referenced on the one hand by thetwo spherical coordinates (hereinafter referred to as V, and V of the point of intersection P with the basic sphere Q on the radius of sphere Q passing by the considered point of the meridian, and, on the other hand, by the distance 6 between said considered point A, of the meridian and said point P of intersection (See FIG. of the enclosed drawings). Thus, the surface is determined by a table of discrepancies or distances 6, for a great number of points of said surface, the distribution of which is chosen to be uniform to allow an easy interpolation; for instance V and V, will be the spherical coordinates of the points of intersection of regularly spaced meridian curves with regularly spaced parallel curves of the basic sphere Q. Then, a high stress resistant steel master pattern of the desired surface is ground, point by point, by means of the diamond wheel grinding machine disclosed in the US. Pat. No. 2,982,058 for the use of which the discrepancy table must be transformed into a grinding table by means of simple calculation taking into account the geometrical features of the machinery such as for instance the diameter of the grinding wheel. Then, this master pattern is reproduced by means of the reproducing machine disclosed in the US. Pat. No. 3,041,789, on a refringent material block to make a lens blank, or a suitable material to make a mould which permits to obtain a lens by casting a polymerizable material, or a hard refractory material used as a stand upon which a glass block is caused to weigh down when put in a temperature regulated furnace. The desired surface in then smoothed by means of the machine disclosed in the U.S. Pat. No. 3,021,647 which does not alter its shape, then polished by means of well known flexible polisher machinery. The same procedure may be adhered to for determining and producing any kind of refracting surface of an ophthalmic lens to obtain a given result. For instance the applicant uses this procedure to determine and industrially produce aspheric aberration correcting surfaces of revolution, the meridian of which needs no longer to be of a known curve. These surfaces lead to a better result which is mainly due to the simplicity and the high precision of the manufacturing process above recalled.

SUMMARY OF THE INVENTION It is the essential object of the present invention to provide a novel type of ophthalmic toric lens of which at least one of its two refracting surfaces constitutes an aberration minimizing surface which, by taking due account of the desired final characteristics of a toric single-focus lens, on the one hand, and on the other hand of the conditions of use of this lens, permits the best correction of the aberrations. The aberration minimizing surface of an ophthalmic lens according to this invention, designed notably for equipping spectacles, is obtained mainly by properly determining the distance or discrepancy between each point of said surface and the corresponding point of a basic sphere, these distances being counted on the radii of said sphere.

To this end, the invention provides an ophthalmic aberration corrected toric lens which is derived from a basic toric lens, said basic lens having on a block of refringent material a spherical refracting surface and a toric refracting surface, said basic lens further having first and second main meridian planes at right angles to one another, said ophthalmic aberration corrected toric lens having,on a block of the said refracting material, two opposite refracting surfaces one of which is identical to one of the two refracting surfaces of said basic lens, while the other refracting surface of said aberration corrected ophthalmic lens is a so-called aberration minimizing surface and is shaped to maintain astigmatism and field curvature aberrations of said ophthalmic lens less than i 0.50 Diopters, said ophthalmic lens further having first and second main meridian planes coincident with said first and second main meridian planes of said basic lens, respectively, said first and second main meridian planes intersecting said aberration minimizing surface along a first and a second meridian curve, respectively, which divide said aberration minimizing surface into four quarters, wherein: said first meridian curve is identical to a meridian curve of a first aspheric surface of revolution adapted to minimize the aberrations of a first spherical lens, the section of said first spherical lens by a meridian plane thereof being identical to the section of said basic lens by said first main meridian plane, said first spherical lens being made of said refringent material, said first meridian curve being determined by a first series of discrepancies e, at several points of said first meridian curve to a reference sphere centered on the optical axis of said ophthalmic lens, said discrepancies a being measured along the radii of said reference sphere upon which are situated said several points, respectively; said second meridian curve is identical to a meridian curve of a second aspheric surface of revolution adapted to minimize the aberrations of a second spherical lens, the section of said second spherical lens by a meridian plane thereof being identical to the section of said basic lens by said second main meridian plane, said second spherical lens being made of said refringent material, said second meridian curve being determined by a second series of discrepancies e, at several points of said second meridian curve to said reference sphere, said discrepancies e, being measured along the radii of said reference sphere upon which are situated said several points, respectively, of said second meridian curve and a random point of any one of said four quarters of the aberration minimizing surface is situated firstly on a radius of said reference sphere which makes an angle V, with said optical axis and lies in a random meridian plane of said aberration minimizing surface which makes an angle w with said first main meridian plane, and secondly at a distance (discrepancy)e from the surface of said reference sphere, a being given by the formula:

where e, is the discrepancy of that one of the points of said first main meridian curve which is situated on a radius of said reference sphere making said angle V, with said optical axis, e is the discrepancy of that one of the points of said second main meridian curve which is situated on a radius of said reference sphere making said angle V, with said optical axis, and flw) is a function of said angle w which varies from when said random meridian plane is coincidentwith said first main meridian plane to 90 when said random meridian plane is coincident with said second main meridian plane, said function being bound to the following conditions:

for W=90 ,f(w)=0 and df(w)/w=0 whereby said one quarter is completely determined, the whole aberration minimizing surface being completed by symmetries about said first and second main meridian planes.

BRIEF DESCRIPTION or THE DRAWINGS Other objects, features and advantages of the present invention will appear more clearly as the following description proceeds with reference to the accompanying drawing illustrating diagrammatically by way of example various forms of embodiment of the ophthalmic lenses according to the present invention. In the drawings:

FIG. 1 illustrates in diagrammatic form an eye with which a corrector lens is associated, this eye looking successively at an object point located at infinity and an object point located at a finite distance;

FIG. 2 is a diagram showing the aberrations under distant-vision conditions with a spherical lens having a l2.00-diopter power, as a function of the angle of vision to the horizontal;

FIG. 3 is a diagram illustrating the method of calculating the discrepancies with respect to a reference sphere for obtaining a meridian, of an aberration minimizing surface of an ophthalmic lens according to the invention;

FIG. 4 is a diagram showing the aberrations of a toric lens of+ 12.00 D (cylinder+ 3.00 D);

FIG. 5 shows the reference system principle used for obtaining a discrepancy table;

FIG. 6 is a diagram illustrating the calculation of the discrepancy at a random point of an aberration minimizing surface of a first type according to the invention;

FIG. 7 is a simplified illustration of the general shape of an aberration minimizing surface of said first type;

FIG. 8 is a discrepancy table of a quarter of an actual exemplary aberration minimizing surface for a toric lens+ 12.00 D (cylinder 3.00 D);

FIG. 9 shows the characteristics of the lens of the actual chosen example, and the intersection of the aberration minimizing surface of sais lens by the two main meridian planes thereof and by an intermediate meridian plane at 45 to the main meridian planes.

FIG. 10 shows isodiscrepancy curves of the aberration minimizing surface of the first type according to the invention, for the chosen example.

FIG. 1 1 gives the performances of a toric lens having the same focal power as that of the chosen example, but corrected according to the previously known method by an aspheric surface of revolution;

FIG. 12 illustrates the results of the correction of aberrations on the spherical surface by a surface of the first type according to the invention;

FIG 13 is a simplified illustration of the general shape of an aberration minimizing surface of a second type according to the present invention;

FIG. 14 is a diagram illustrating the calculation of the discrepancy at a random point of an aberration minimizing surface of said second type;

FIG. 15 gives the general characteristics of a second exemplary lens 14.00 D (cylinder 2.00 D) corrected by an aberration minimizing surface of said second type, and shows the -curves of intersection of the aberration minimizing surface of said second exemplary lens by the two main meridian planes thereof and by an intermediate meridian plane at 45 to the main meridian planes;

FIG. 16 is the discrepancy table of a surface of the second type according to the invention adapted to correct or minimize the aberrations of the lens of the second chosen example, the discrepancies being given with respect to the concave toric surface of the basic toric lens, in the reference system of FIG. 5;

FIG. 17 shows isodiscrepancy curves illustrating the deformation applied to the concave toric surface of the lens of the second chosen example to obtain its aberration minimizing surface; and

FIG. 18 is a front view of a lens of which the upper and lower halves are corrected for aberrations prevailing in distant vision and reading vision, respectively.

DESCRIPTION OF THE PREFERRED EMBODIMENTS Referring first to FIG. 1, an eye 1 looks at a point located at infinity through its corrector lens 2 having an optical axis 3 passing through the center of rotation of the eye, the axis of vision forming an angle U with the optical axis 3. Assuming that if U 0 the ametropia correction is perfect, a point at infinity gives an image (R,,) which, when received by the optical instrument constituted by the human eye, forms an image (2,) upon the retina. When, without altering its accommodation, the eye rotates about 0, a point at infinity will be seen clearly, irrespective of the value of angle U, if the image R of this point describes a sphere having a center 0 and a radius OR.

In practice, if the lens has to be shaped to have a spherical surface, for example for any value of U other than 0, the light ray from the object point lying at infinity will bear on a sagittal focus S and a tangential focus T, and the circle of least confusion lies at I. The field curvature IR and the astigmatism TS are the main aberrations disturbing the correction of the eyes ametropia.

FIG. 2 illustrates the aberrations of a spherical power lens of 12.00 diopters as a function of the angle U for infinity observation. These curves illustrate not the variation in the position of the various images but the variaion of the reciprocals of the distances in meters from said images to a same reference point.

To simplify the following calculations the point of reference is selected as customary at the intersection of the central ray of the direction of vision with the circle centered at 0 and having a radius CH of which the value, for all practical purposes, is of the order of 27 to 28 millimeters (FIG. 1). This point is denoted K for distant or infinity vision and G when the eye looks at an object point M. Consequently, these reciprocals are as follows:

l/HRo For infinity vision, the eye does not accommodate and F is a constant power.

FIG. 2 shows that a 12.00-diopter spherical lens, if U 30", has a field curvature c BC= F,-F 0.65 D, and an astigmatism a AD =F F 4.50 D.

Let us consider a toric high power ophthalmic lens 12.00 D (cylinder 3.00 D) to becorrected for aberrations and of which the concave refracting surface is spherical. This toric lens has aberrations represented in FIG. 4 as usual in the two main meridians.

The sagittal power remains close to the desired value, that is to say, in FIG. 1, S remains close to R or KS does not differ very much from KR.

The tangential power increases with U, that is to say KT decreases very much from its value HRo when U 0 (FIG. 1). The rate of increasing is very high and is responsible for the narrowing of the field of view of such an aberration uncorrected lens.

In FIG. 1, for a spherical power lens, the reduction of astigmatism can be illustrated by bringing KT close to KS and the reduction of field curvature by bringing (KI KS)/2 K! close to KR. This illustration can be easily transposed to illustrate the correction of a toric lens as it is usual in the art. Due to the fact that an ophthalmic lens is a simple optical system which has a too small number of independent parameters it is well known in the art that the correction of the aberrations leads to a compromise. Field curvature error and parasitic astigmatism can only be brought between acceptable limits which, for high power lenses and by way of illustrating example, are usually 1 0.50 Diopters for U 30.

To correct the aberrations of the toric lens of the above example, one can modify, for instance, the shape of its concave spherical refracting surface, to reduce the tangential power while reducing or maintaining the sagittal power within said acceptable limits, and to obtain variations of FT and FS as functions of angle u adapted to bring the field curvature within said acceptable limits.

This is obtained by optical calculations as follows.

Referring to FIG. 3, let us consider the section of the to be corrected toric lens by its 12.00 D main meridian plane. Assuming that this section is rotated around the optical axis of the lens, it will generate a spherical single focus 12.00 D lens which is made of the same refringent material as that of said toric lens and has a meridian section identical to that of the to be corrected toric lens by the 12.00 D main meridian plane thereof. Considering now this spherical 12.00 D lens,for as many values of angle U as desired, the tangential and sagittal power along said meridian section l/KT and l/KS) can be easily calculated by usual optical calculation using the parameters represented in FIG. 3. Thus, for each selected value of angle U one can calculate (l/KT) (I/KR) which is the excess of power to be cut off from the tangential power.

Let us consider a reference sphere Q of which the center is 00 and the radius r0, and which is tangent to the concave spherical surface of the lens.

At every value of angle U corresponds a point A, of the meridian curve of the desired aberration minimizing surface.

At every value of the angle U corresponds a power to be cut off from tangential power along the sight axis to which corresponds a power to be cut off from the tangential power along the axis A,O,,. Usual optical calculations permit to obtain the tangential power and the excess power along A,O,, from tangential power and excess power along the sight axis.

For every point A it is an easy matter to calculate the decreasing of the radius of curvature of the concave meridian curve which is needed to cut off the excess tangential power from the tangential power.

So, step by step, a series of values is obtained which gives for every point A, the value of the radius of curvature of the concave meridian curve.

This leads to the profile of said concave meridian curve. The aberration minimizing surface of said spherical 12.00 D lens is of course of revolution. It is easy to calculate the sagittal radius of this surface along AiOo.

In the to be corrected toric lens of 12.09 d (cylinder 3.00 D) the portion of the desired aberration minimizing surface on either side of and in the vicinity of the 12.00 D main meridian plane can be considered, in first approximation, identical to the aberration minimizing surface of the spherical 12.00 D lens along a meridian of which the values of the tangential and sagittal radii are known at least at every chosen point A, of said concave meridian curve.

Simple optical calculations lead to the tangential and sagittal powers along the sight axis for the corresponding values of U.

Due to necessary approximations the profile of the meridian curve of the concave aberration minimizing surface of the toric lens, in the 12.00 D meridian plane, is obtained after several calculations as hereinabove explained which permits to know the influence of this profile on the tangential and sagittal power variations and to choose the best possible compromise. This profile is known as a series of values of the radii of curvature of the meridian curve at every point of said meridian curve corresponding to every chosen point A that is as a function of angle U. It is an easy step to obtain the actual shape of this curve and to determine the discrepancies or distances 6 to the basic sphere Q of this curve at every point A The meridian curve in the 12.00 D main meridian plane of the desired aberration minimizing surface is thus known as a first series of discrepancies to the reference sphere Q in as many points as desired.

To determine the meridian curve in the 15.00 D main meridian plane which is at right angles to the 12.00 main meridian plane, one follows exactly the same procedure. This leads to a second series of discrepancies to the reference sphere Q in as many points as desired.

FIG. 5 illustrates the principle of the reference system used and how the discrepancies are posted up into a table. Usually, the points A, are chosen to be spaced from one another every 2 millimeters measured on the surface of the reference sphere Q, and are represented on the table in a point of which the coordinates s and 5,, corresponds to the curvilinear distances S, and 8,, measured on the surface of the sphere O in the represented polar coordinates system.

At this point of the explanations the series of discrepancies of the 12.00 D main meridian of the aberration minimizing surface according to the invention is posted up into the central vertical column of the table, and the series of discrepancies of the 15.00 D main meridian of the same aberration minimizing surface is posted up into the horizontal central line of the table.

To obtain the complete discrepancy table of the aberration correcting surface according .to the invention one proceeds as follows:

At a given distance s to the center of the table correspond a point on the central column s, s, s 0 and a point on the central line (s,, 0, s, s). Let us call those two points the corresponding points of the central column and central line of the table. A series of differences between the discrepancies of these corresponding points for different values of s is established.

The two main meridian planes of the toric lens divide the desired aberration minimizing surface into four quarter. The discrepancy at a point situated in any one of said four quarters at a distance s from the center of the table and belonging to the curve of intersection of the aberration minimizing surface by a meridian plane making an angle w with the vertical meridian plane 0 P Y (FIG. 6) is given by the formula w 1+( y .r)[ f( where a is the discrepancy at said point of the intermediate meridian curve situated at the distance s from the center of the table, 6,, is the discrepancy at the point of the central vertical column located at a distance s from the center of the table, c is the discrepancy at the point of the central horizontal line located at a distance s from the center of the table, and f (w) is a chosen function of the angle w which satisfies the following conditions df(w)/dw O,f(w) l for w 0 w is allowed to take any value between 0 and the table being then completed by symmetries with respect to the two main meridians.

f(w) is determined as follows:

Along one or several intermediate meridians corresponding to one or several values of angle w, several profiles corresponding to several series of values of e are tried to obtain different corrections of aberrations along said intermediate meridians. This leads to the then, it is easy, by interpolations, to obtain the discrepancy at any point of the table of discrepancies of the surface according to the invention. The abovedescribed method of determining the aberration minimizing surface of a toric lens leads to meridians for which no hypotheses have been made as to their shape; experience teaches that in the case of high-power lenses the resulting tables of divergences lead to curves of which the shapes can be described as elliptic shapes,at least for simplification sake of the explanation. Thus, an example affording a clearer understanding of the shape of the aberration minimizing surface can be given with reference to FIG. 7. Since the aberration minimizing surface is concave in this example, these ellipses or elliptic portions revolve about their minor axis and admit the radius (r,,) of the concave spherical surface of the lens as the radius of the osculating circle at the pole P of the aberration minimizing surface.

Thus, in the first main meridian M h the ellipse E will be characterized by parameters a, and b the values of which, on the one hand, are chosen so that ellipse E approximates the above-determined main meridian curve corresponding to the first series of discrepancies, and, on the other hand, satisfy the well known relation between the radius of the osculating circle at the tip of the minor axis of an ellipse and the parameters thereof,

that is, in the present case: af/b r Similarly, in the second main meridian M the ellipse Ii will be characterized by a and b such that af/b r,,. A random meridian curve m, of the aspheric surface will thus be an ellipse characterized by a, and b, such that, on the one hand, afi/b, r and, on the other hand, a, A(w) and b, B(w), where w denotes the angle formed between the meridian involved and, for instance, the first main meridian, and A(w) and B(w) are two functions of w, these two functions being such that the discrepancy to the reference sphere Q at any point A, of meridian curve m satisfies the above-mentioned formula I The aberration minimizing surface will thus appear as constituting the envelope of an ellipse E, revolving about its minor axis and undergoing a deformation between two endmost ellipses E and E while preserving the same osculating circle at its vertex or pole P.

FIG. 8 is the actual discrepancy table of the concave aberration minimizing surface of the lens the actual characteristics of which are given in FIG. 9. This discrepancy table is in fact a discrepancy table of a quarter of the aberration minimizing surface limited to one-half of the il2.00 D main meridian corresponding to the column 50 of the table and to one-half of the i 15.00 D main meridian corresponding to the line 50 of the table. These discrepancies are given in microns for curvilinear distances on the surface of sphere Q of 4 mm between two adjacent points. The intermediate values are easily obtained by interpolation, the discrepancy table of the complete surface, of course being obtained by symmetries with respect to the two main meridians since this surface is symmetrical with respect to its two main meridian planes.

In FIG. 9 is given a representation of the profile of the intersection of the surface according to the invention by the two main meridian planes of the lens and by the intermediate meridian corresponding to w 45, the radius of the reference sphere being conventionally assumed as having an infinite value in this FIG. 9.

FIG. 10 shows the isodiscrepancy curves of one-half of the surface according to the invention which appears as a surface having a spherical central portion which is gradually deformed towards the outer'periphery, and admitting as its planes of symmetry the planes of the main meridians of the toric lens, thus assuming the presence of a toric character in this peripheral portion.

For this reason, the aberration minimizing surfaces illustrated in FIG. 7 which correspond to the above description, are surfaces of a first type of aberration minimizing surface according to the invention and will be referred to as atoric sphere" aberration minimizing surfaces.

The interest of such aberration minimizing surfaces is illustrated by the actual results obtained, readily measurable and represented in FIG. 12 as compared to the results hitherto accepted represented in FIG. 11. These results correspond to the actual chosen example.

Let us consider as another example an aberrationuncorrected toric lens consisting of a convex spherical refracting surface and a concave torical refracting surface.

To correct the aberrations of such a lens one can modify the shape of the concave torical surface of the lens into an aberration minimizing surface of a second type. The explanations and the calculation procedure given hereinabove are readily transposable here.

As it has already been mentioned hereinabove, to simplify the explanations and to give an idea of the shape of an aberration minimizing surface of the second type according to the present invention, let us assume that the meridian curves are or approximate e]- lipses (FIG. 13). The main meridian curve m will be an ellipse E characterized by parameters a and 11 such that a /b r,, the main meridian curve m being an ellipse E characterized by parameters a and b such-that in this case az /bg r and a random meridian curve m being an ellipse E, characterized by parameters a, and b, such that 03/11, n, wherein r, is determined by the elliptic indicatrix of the toric surface at its vertex P, i.e. the curve representing r, H (w) which at the vertex P of the uncorrected concave toric surface is an ellipse. As in the foregoing, a, and b, are two functions of w which vary respectively from a to a and from b to b these two functions of w being such that the discrepancy to the reference sphere Q at any point A, of the random intermediate meridian curve satisfies the abovementioned formula (1) considered with reference to FIG. 14 which corresponds to FIG. 6.

Let us consider the actual example of a 14.00 cylinder 2.00 D) lens of which the characteristics are represented FIG. 15.

In the reference system represented in FIG. 5, one can easily calculate the table of discrepancies of the concave toric refracting surface (r 168 mm and r 504 mm) with respect to the reference sphere Q which is tangent to said toric surface at its point of intersection with the optical axis of the lens and has a radius r0 168.00 mm. It will be noted that in the 14.00 D main meridian, the series of discrepancies contains zero only since the radius r, of the concave meridian is 168.00 mm.

The above-mentioned modification of the shape of this toric concave surface to obtain the aberration minimizing surface is given by the discrepancy table of FIG. 16. More precisely, the discrepancy values plotted in table of FIG. l6corresponds to discrepancies with respect to the aberration-uncorrected toric surface which are measured along the radii of the reference sphere O. This discrepancy table is in fact a discrepancy table of a quarter of the aberration minimizing surface limited to one-half of the 14.00 main meridian plane (column 50) and to one-half of the 16.00D main meridian plane (line 50). These discrepancies are given in microns and for curve distances on the sphere Q of 4 mm. between two adjacent points. The intermediate values can be easily obtained by mere interpolation and the complete table can be easily obtained by symmetries with respect to the two main meridians of the toric lens since this surface is symmetrical with respect to these two main meridian planes.

On FIG. 15 is given a representation of the profile of the deformation of the toric surface (this toric surface being conventionally assumed to be a plane) in the two main meridians and in the intermediate meridian corresponding to w =45".

FIG. 17 shows the isodiscrepancy curves of this deformation brought to the concave toric surface. It points out that this deformation is of a nature identical to the nature of the deformation of the concave spherical surfaceleading to the aberration minimizing surface of the first type according to the invention.

To obtain the discrepancy table of the concave aberration minimizing surface with respect to the sphere Q, one has to add for every point of the desired aberration minimizing surface having given coordinates the discrepancy with respect to sphere Q of the point of the uncorrected toric surface having these given coordinates and the discrepancy corresponding to the deformation to be applied to this point of the uncorrected toric surface to obtain the point of given coordinates of the desired aberration minimizing surface. In other words, one has merely to superimpose the two discrepancy tables and to add the discrepancies point by point.

It will be seen that the aberration minimizing surface is merged into the initial toric surface in the vicinity of the central zone of the lens and evolves towards the edges while preserving its toric character, notably by preserving for its planes of symmetry the main planes of the lens. For this reason, these aberration minimizing surfaces of the second type according to the invention will be referred to as surfaces of the atoric tore type.

It will be noted that ophthalmic toric lenses, according to the invention, which are derived from a basic toric lens, can be obtained by correcting the aberrations of said basic lens either by altering the shape of its spherical surface into a first type surface called atoric sphere" surface, or by altering its toric surface into a second type surface called atoric tore surface. The corrections thus obtained are equivalent and the choice between these two types is made from manufacturing considerations.

In the foregoing, it has been assumed in the two examples that the aberration minimizing surface was obtained by altering the shape of the concave spherical or toric surface of the basic toric surface from which it derives into a surface of the first or second type, respectively, but said aberration minimizing surface could as well be obtained by altering the convex toric or spherical surface, as may be the case, of said basic surface into a surface of the second or first type, respectively, the same explanations applying also here. As a matter of fact, the aberration minimizing surfaces of the first and second type, which are diagrammatically illustrated in FIGS. 6 and 7 and FIGS. 13 and 14, respectively, are represented alone and could constitute the concave refracting surface of the toric lens as well as the convex refracting surface thereof.

In all the foregoing the observation of an object point at infinity was contemplated. Now when the eye is capable of accommodation such toric lenses can also be used for reading. In this case they have different aberrations which are sometimes not sufficiently corrected by the distortion corresponding to. infinity vision.

As shown in FIG. 1, it is an easy matter to determine according to the same principles a lens corrected for observing at a finite distance d MN It is only necessary to adhere to the above-described method.

It is even possible, without departing from the scope of the present invention, to provide ophthalmic lenses provided on at least one face with aberration minimizing surface areas determined respectively in such a manner as to correct the aberrations corresponding to a plurality of vision distances. The simplest case illustrated in FIG. 18 is an unifocal lens of which the upper half is corrected for aberrations prevailing in distant vision VL and the lower half for aberrations prevailing in reading vision (VP); the line separating these two surfaces being for example discontinuous as in the case of a bifocal lens.

To manufacture lenses according to the invention, one can resort to the method and machinery recalled in the foreword of the present application. Usually these high-power lenses are thick and to save weight one prefers to manufacture them by casting a polymerizable material between conveniently shaped mold elements.

It would not constitute a departure from the invention to direct the correction to field curvature only, parasitic astigmatism only, distortion only or to any compromise between these aberrations.

Furthermore, it would not lie outside the scope of the invention to associate in a same lens two aberration correcting surfaces in order to obtain a better correction of the aberrations or to incorporate the correction of another type of aberration.

What I claim is:

1. An ophthalmic aberration corrected toric lens which is derived from a basic toric lens, said basic lens having on a block of refringent material a spherical refracting surface and a toric refracting surface, said basic lens further having first and second main meridian planes at right angles to one another, said ophthalmic aberration corrected toric lens having, on a block of the said refracting material, two opposite refracting surfaces one of which is identical to one of the two refracting surfaces of said basic lens, while the other refracting surface of said aberration corrected ophthalmic lens is a so-called aberration minimizing surface and is shaped to maintain astigmatism and field curvature aberrations of said ophthalmic lens less than i 0.50 Diopters, said ophthalmic lens further having first and second main meridian planes coincident with said first and second main meridian planes of said basic lens, respectively, said first and second main meridian planes intersecting said aberration minimizing surface along a first and a second meridian curve, respectively, which divide said aberration minimizing surface into four quarters, wherein: said first meridian curve is identical to a meridian curve of a first aspheric surface of revolution adapted to minimize the aberrations of a first spherical lens, the section of said first spherical lens by a meridian plane thereof being identical to the section of said basic lens by said first main meridian plane, said first spherical lens being made of said refringent material, said first meridian curve being determined by a first series of discrepancies e, at several points of said first meridian curve to a reference sphere centered on the optical axis of said ophthalmic lens, said discrepancies a, being measured along the radii of said reference sphere upon which are situated said several points, respectively; said second meridian curve is identical to a meridian curve of a second aspheric surface of revolution adapted to minimize the aberr'ations of a second spherical lens, the section of said second spherical lens by a meridian plane thereof being identical to the section of said basic lens by said second main meridian plane, said second spherical lens being made of said refringent material, said second meridian curve being determined by a second series of discrepancies e at several points of said second meridian curve to said reference sphere, said discrepancies 6,, being measured along the radii of said reference sphere upon which are situated said several points, respectively, of said second meridian curve and a random point of any one of said four quarters of the aberration minimizing surface is situated firstly on a radius of said reference sphere which makes an angle V, with said optical axis and lies in a random meridian plane of said aberration minimizing surface which makes an angle w with said first main meridian plane, and secondly at a distance (discrepancy) e, from the surface of said reference sphere, e, being given by the formula:

where 6,, is the discrepancy of that one of the points of said first main meridian curve which is situated on a radius of said reference sphere making said angle V, with said optical axis, e, is the discrepancy of that one of the points of said second main meridian curve which is situated on a radius of said reference sphere making said angle V, with said optical axis, and f(w) is a function of said angle w which varies from when said random meridian plane is coincident with said first main meridian plane to 90 when said random meridian plane is coincident with said second main meridian plane, said function being bound to the following conditions:

for w 0,f(w) l and df(w)/dw =0 for w 90,f(w) 0 and df(w)/dw 0 whereby said one quarter is completely determined, the whole aberration minimizing surface being completed by symmetries about said first and second main meridian planes.

2. Ophthalmic toric a convex refracting surface and a concave refracting surface, and which is derived from a basic toric lens comprising a convex toric refracting surface and a concave spherical refracting surface, wherein said aberration minimizing surface is the concave surface of the ophthalmic toric lens and has, in the close vicinity of the optical axis, a spherical central portion identical to the relevant central portion of said concave spherical refracting surface, said aberration minimizing surface being gradually deformed towards the outer periphery thereof while admitting as planes of symmetry said first and second main meridian planes, said aberration minimizing surface thereby presenting a toric character in the peripheral portion thereof.

3. Ophthalmic toric lens according to claim 1, having a convex refracting surface and a concave refracting surface, and which is derived from a basic toric lens comprising a convex spherical refracting surface and a lens according to claim 1, having concave toric refracting surface, wherein said aberration minimizing surface is the concave surface of the ophthalmic toric lens and has in the close vicinity of the optical axis a toric central portion identical to the relevant central portion of said concave toric refracting surface, said aberration minimizing surface being gradually deformed towards the outer periphery thereof while still admitting as planes of symmetry said first and second main meridian planes and thereby preservin a toric character. I

4. Oph almic toric lens according to claim 1, having a concave refracting surface and a convex refracting surface, and which is derived from a basic toric lens comprising a concave toric refracting surface and a convex spherical refracting surface, wherein said aberration miriimizing surface is the convex surface of the ophthalmic toric lens and has, in the close vicinity of the optical axis, a spherical central portion identical to the relevant central portion of said convex spherical refracting surface, said aberration minimizing surface being gradually deformed towards the outer periphery thereof while admitting as planes of symmetry said first and second main meridian planes, said aberration minimizing surface thereby presenting a toric character in the peripheral portion thereof.

5. Ophthalmic toric lens according to claim 1, having a concave refracting surface and a convex refracting surface, and which is derived from a basic toric lens comprising a concave spherical refracting surface and a convex toric refracting surface, wherein said aberration minimizing surface is the convex surface of the ophthalmic toric lens and has in the close vicinity of the optical axis a toric central portion identical to the relevant central portion of said convex toric refracting surface, said aberration minimizing surface being gradually deformed towards the outer periphery thereof while still admitting as planes of symmetry said first and second main meridian planes and thereby preserving a toric character.

6. Ophthalmic toric lens according to claim 1, wherein the aberrations which are minimized are those prevailing for an infinite distance of vision.

7. Ophthalmic toric lens according to claim 1, wherein the aberrations which are minimized are those prevailing for a finite distance of vision.

8 Ophthalmic toric lens according to claim 1, wherein said aberration minimizing surface is composed of several adjacent aberration minimizing surface areas in each of which the aberrations which are minimized are those prevailing for a predetermined distance of vision.

wherein said function f(w) is cos w.

* t (i l 

1. An ophthalmic aberration corrected toric lens which is derived from a basic toric lens, said basic lens having on a block of refringent material a spherical refracting surface and a toric refracting surface, said basic lens further having first and second main meridian planes at right angles to one another, said ophthalmic aberration corrected toric lens having, on a block of the said refracting material, two opposite refracting surfaces one of which is identical to one of the two refracting surfaces of said basic lens, while the other refracting surface of said aberration corrected ophthalmic lens is a so-called aberration minimizing surface and is shaped to maintain astigmatism and field curvature aberrations of said ophthalmic lens less than + OR - 0.50 Diopters, said ophthalmic lens further having first and second main meridian planes coincident with said first and second main meridian planes of said basic lens, respectively, said first and second main meridian planes intersecting said aberration minimizing surface along a first and a second meridian curve, respectively, which divide said aberration minimizing surface into four quarters, wherein: said first meridian curve is identical to a meridian curve of a first aspheric surface of revolution adapted to minimize the aberrations of a first spherical lens, the section of said first spherical lens by a meridian plane thereof being identical to the section of said basic lens by said first main meridian plane, said first spherical lens being made of said refringent material, said first meridian curve being determined by a first series of discrepancies Epsilon x at several points of said first meridian curve to a reference sphere centered on the optical axis of said ophthalmic lens, said discrepancies Epsilon x being measured along the radii of said reference sphere upon which are situated said several points, respectively; said second meridian curve is identical to a meridian curve of a second aspheric surface of revolution adapted to minimize the aberrations of a second spherical lens, the section of said second spherical lens by a meridian plane thereof being identical To the section of said basic lens by said second main meridian plane, said second spherical lens being made of said refringent material, said second meridian curve being determined by a second series of discrepancies Epsilon y at several points of said second meridian curve to said reference sphere, said discrepancies Epsilon y being measured along the radii of said reference sphere upon which are situated said several points, respectively, of said second meridian curve and a random point of any one of said four quarters of the aberration minimizing surface is situated firstly on a radius of said reference sphere which makes an angle Vi with said optical axis and lies in a random meridian plane of said aberration minimizing surface which makes an angle w with said first main meridian plane, and secondly at a distance (discrepancy) Epsilon wi from the surface of said reference sphere, Epsilon wi being given by the formula: Epsilon wi Epsilon xi + ( Epsilon yi - Epsilon xi) (1 - f(w) ) where Epsilon xi is the discrepancy of that one of the points of said first main meridian curve which is situated on a radius of said reference sphere making said angle Vi with said optical axis, Epsilon yi is the discrepancy of that one of the points of said second main meridian curve which is situated on a radius of said reference sphere making said angle Vi with said optical axis, and f(w) is a function of said angle w which varies from 0* when said random meridian plane is coincident with said first main meridian plane to 90* when said random meridian plane is coincident with said second main meridian plane, said function being bound to the following conditions: for w 0*, f (w) 1 and df(w)/dw o for w 90*, f (w) 0 and df(w)/dw 0 whereby said one quarter is completely determined, the whole aberration minimizing surface being completed by symmetries about said first and second main meridian planes.
 2. Ophthalmic toric lens according to claim 1, having a convex refracting surface and a concave refracting surface, and which is derived from a basic toric lens comprising a convex toric refracting surface and a concave spherical refracting surface, wherein said aberration minimizing surface is the concave surface of the ophthalmic toric lens and has, in the close vicinity of the optical axis, a spherical central portion identical to the relevant central portion of said concave spherical refracting surface, said aberration minimizing surface being gradually deformed towards the outer periphery thereof while admitting as planes of symmetry said first and second main meridian planes, said aberration minimizing surface thereby presenting a toric character in the peripheral portion thereof.
 3. Ophthalmic toric lens according to claim 1, having a convex refracting surface and a concave refracting surface, and which is derived from a basic toric lens comprising a convex spherical refracting surface and a concave toric refracting surface, wherein said aberration minimizing surface is the concave surface of the ophthalmic toric lens and has in the close vicinity of the optical axis a toric central portion identical to the relevant central portion of said concave toric refracting surface, said aberration minimizing surface being gradually deformed towards the outer periphery thereof while still admitting as planes of symmetry said first and second main meridian planes and thereby preserving a toric character.
 4. Ophthalmic toric lens according to claim 1, having a concave refracting surface and a convex refracting surface, and which is derived from a basic toric lens comprising a concave toric refracting surface and a convex spherical refracting surface, wherein said aberration minimizing surface is the convex Surface of the ophthalmic toric lens and has, in the close vicinity of the optical axis, a spherical central portion identical to the relevant central portion of said convex spherical refracting surface, said aberration minimizing surface being gradually deformed towards the outer periphery thereof while admitting as planes of symmetry said first and second main meridian planes, said aberration minimizing surface thereby presenting a toric character in the peripheral portion thereof.
 5. Ophthalmic toric lens according to claim 1, having a concave refracting surface and a convex refracting surface, and which is derived from a basic toric lens comprising a concave spherical refracting surface and a convex toric refracting surface, wherein said aberration minimizing surface is the convex surface of the ophthalmic toric lens and has in the close vicinity of the optical axis a toric central portion identical to the relevant central portion of said convex toric refracting surface, said aberration minimizing surface being gradually deformed towards the outer periphery thereof while still admitting as planes of symmetry said first and second main meridian planes and thereby preserving a toric character.
 6. Ophthalmic toric lens according to claim 1, wherein the aberrations which are minimized are those prevailing for an infinite distance of vision.
 7. Ophthalmic toric lens according to claim 1, wherein the aberrations which are minimized are those prevailing for a finite distance of vision.
 8. Ophthalmic toric lens according to claim 1, wherein said aberration minimizing surface is composed of several adjacent aberration minimizing surface areas in each of which the aberrations which are minimized are those prevailing for a predetermined distance of vision.
 9. Ophthalmic toric lens according to claim 1, wherein said function f(w) is cos2 w. 